Evaluating exponential functions for negative inputs can be done using the following steps:

1. Understand the Exponential Function: An exponential function is a mathematical function of the form f(x) = a^x, where 'a' is a positive real number, not equal to 1, and 'x' is any real number.

2. Negative Inputs: When we talk about negative inputs, we are referring to the 'x' in the function f(x) = a^x. So, if we have a function like f(x) = 2^x, and we want to evaluate it for x = -3, we would plug -3 in for x, giving us 2^-3.

3. Reciprocal Rule: The key to evaluating exponential functions for negative inputs is understanding that a^-n = 1/a^n. This is known as the reciprocal rule. So, if we have 2^-3, we can rewrite this as 1/2^3.

4. Evaluate: Now, we simply evaluate the expression. In our example, 2^3 = 8, so 1/2^3 = 1/8.

5. Conclusion: Therefore, the value of the function f(x) = 2^x at x = -3 is 1/8.

Remember, this strategy works for any base 'a' and any negative exponent 'x'. The key is understanding the reciprocal rule and applying it correctly.

Question

Evaluating exponential functions for negative inputs can be done using the following steps:

1. Understand the Exponential Function: An exponential function is a mathematical function of the form f(x) = a^x, where 'a' is a positive real number, not equal to 1, and 'x' is any real number.

2. Negative Inputs: When we talk about negative inputs, we are referring to the 'x' in the function f(x) = a^x. So, if we have a function like f(x) = 2^x, and we want to evaluate it for x = -3, we would plug -3 in for x, giving us 2^-3.

3. Reciprocal Rule: The key to evaluating exponential functions for negative inputs is understanding that a^-n = 1/a^n. This is known as the reciprocal rule. So, if we have 2^-3, we can rewrite this as 1/2^3.

4. Evaluate: Now, we simply evaluate the expression. In our example, 2^3 = 8, so 1/2^3 = 1/8.

5. Conclusion: Therefore, the value of the function f(x) = 2^x at x = -3 is 1/8.

Remember, this strategy works for any base 'a' and any negative exponent 'x'. The key is understanding the reciprocal rule and applying it correctly.

Knowee AI · Accepted Answer

Evaluating exponential functions for negative inputs can be done using the following steps:

1. Understand the Exponential Function: An exponential function is a mathematical function of the form f(x) = a^x, where 'a' is a positive real number, not equal to 1, and 'x' is any real number.

2. Negative Inputs: When we talk about negative inputs, we are referring to the 'x' in the function f(x) = a^x. So, if we have a function like f(x) = 2^x, and we want to evaluate it for x = -3, we would plug -3 in for x, giving us 2^-3.

3. Reciprocal Rule: The key to evaluating exponential functions for negative inputs is understanding that a^-n = 1/a^n. This is known as the reciprocal rule. So, if we have 2^-3, we can rewrite this as 1/2^3.

4. Evaluate: Now, we simply evaluate the expression. In our example, 2^3 = 8, so 1/2^3 = 1/8.

5. Conclusion: Therefore, the value of the function f(x) = 2^x at x = -3 is 1/8.

Remember, this strategy works for any base 'a' and any negative exponent 'x'. The key is understanding the reciprocal rule and applying it correctly.

Describe a strategy for evaluating exponential functions for negative inputs.Use the examples if they help with your thinking.

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Describe a strategy for evaluating exponential functions for negative inputs.

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